HAZIMA, Syria (Reuters) -- The few bullet-marked schools Islamic State did not flatten or booby trap around its former Syrian stronghold of Raqqa are buzzing for the first time in years with the sound of children learning.

In the village of Hazima, north of Raqqa, teachers gave ad-hoc alphabet lessons to crammed classrooms on a recent summer's day before the start of term.

"Right now, the most important thing is to get children into class," said teacher Ahmed al-Ahmed, standing next to a hole in the school stairwell left by a mine blast that wounded a colleague.

The ultra-hardline Islamic State closed this school and many others in northern Syria after it seized control of the region in 2014, three years into the country's civil war. Instead it taught children extremist thought in mosques.

But now that the group has been ousted from most territory it held in and around Raqqa by a U.S.-backed military alliance, the Syrian Democratic Forces (SDF), a growing debate over education points to the ethnic tensions expected to follow.

What is taught in areas under the control of the SDF, which includes Arab militias but is dominated by the Kurdish YPG, is one of many questions over how predominantly Arab parts of northern Syria will be run as they come into the Kurdish fold.

Schools around Raqqa will this year teach a new curriculum that is based on old textbooks but erases the Baathist ideology of President Bashar al-Assad, a decision agreed on by Arab and Kurdish teachers alike.

But an official in the SDF has floated the immediate introduction of Kurdish lessons in Raqqa schools, an idea that makes local officials bristle.

In contrast with other areas under SDF control that have for years taught Kurdish, there are no plans yet to teach the language in mostly Arab Raqqa.

Officials say it would need broad consensus, hinting at concerns that its introduction too quickly would cause unrest.

"We wouldn't object to Kurdish teaching. But if it's imposed on schools then there will be problems," Ahmed said.

RESENTMENT OVER KURDISH POWER

The YPG has held areas of northeast Syria since early in the six-year-old war which are now under a self-run administration opposed by Assad, who holds the main population centers in the west and is also advancing against Islamic State, and Turkey, a YPG foe which borders Syria. Raqqa is likely to join the administration, officials say.

All ethnic groups are represented in the local bodies that run majority Arab regions captured by the SDF as it ousted IS fighters but critics say Kurds dominate decision-making.

Reuters interviews with SDF officials and local authorities suggest resentment over Kurdish power is brewing over education plans.

A senior SDF adviser and coordinator with the U.S. coalition said he believed Kurdish would be taught to Kurdish pupils around Raqqa this year, following the model for other schools in SDF territory.

"No one has opposed this ... every (ethnic) group has the right to study in its own language," Amed Sido said via the internet.

Officials in the Raqqa Civil Council, the newly-formed local governing body, were taken aback.

"No, that won't happen without consultations with us and agreement in the council," Ammar Hussein, an education committee official, said at its office in the town of Ain Issa. "For now it's in Arabic, with English and French lessons."

Echoing several council members, he said Kurdish would be taught only if families requested it, there were enough qualified teachers and the Arab-Kurdish council approved it.

"If the people here agree ... there won't be any objection," said Ali Shanna, another education committee official. "But the Kurd knows the Kurdish language, why does he need to learn it?"

A former Kurdish teacher privately derided Shanna's comments.

"I hate that attitude. It's ignorance, it's the same thinking as Daesh (Islamic State)," said the teacher, who had been jailed under Assad for writing a Kurdish-language journal.

FEAR OF UNREST

The sensitivity over language has already caused unrest in Hasaka to the northeast, an area controlled for years by the YPG where a new curriculum is taught in Arabic and Kurdish, both now official languages. In demonstrations reported by a monitoring group, protesters called for Arab children not to have to learn Kurdish.

Mostafa Bali, an SDF official, said there was no intention to force Kurdish on Arabs, or to suppress Arabic.

"We don't support racism over language. But there are many Kurds who would like to see Arabic teaching banned in Kurdish areas as revenge for the Baath (teaching)," he said.

The Baathist curriculum championed Arab nationalism over ethnic identity. Kurdish pupils were punished for speaking their mother tongue in school playgrounds. Now, even in some Arab-majority towns, Kurds are taught Kurdish.

Officials in Raqqa are determined to do things their way, regardless of what they say are potential military threats from Assad or neighboring Turkey.

"We won't let Turkey or anyone else interfere in our internal affairs. We decide what we'll teach or not teach," Leila Mostafa, the Kurdish co-president of the Raqqa Civil Council said.

At Hazima school, teachers worry about both the legacy left by Islamic State and Assad, and future political upheaval.

The teachers say "racist" Baathist modules help fuel Syria's conflict and are anxious to begin the new curriculum.

"It's urgent we start teaching. The next phase will be difficult - there'll be a reckoning between factions," Ahmed al-Ahmed said, without specifying which groups he was referring to. "A reckoning, in general."